Question

suppose xy=-1 and dy/dt=4. Find dx/dt when x=-3

Answer 1

can u help me plz

Answer 2

xy=-1
\[x \frac{ dy }{ dt }+y \frac{ dx }{ dt }=0\]
when x=-3
-3*y=-1
\[y=\frac{ -1 }{ -3 }=\frac{ 1 }{ 3 }\]
\[\frac{ dy }{ dt }=4\]
plug all the values i.e.,x=-3
y=1/3
dy/dt=1/3
then find dx/dt

Answer 3

or you can do like this
\[x \frac{ dy }{ dt }+y \frac{ dx }{ dt }=0\]
multiply by x
\[x^2\frac{ dy }{ dt }+xy \frac{ dx }{ dt }=0\]
\[(-3)^2*4+(-1)\frac{ dx }{ dt }=0,\]
\[\frac{ dx }{ dt }=?\]

Answer 4

Okay that makes sense! I got 36 which is the correct answer. Thank you!!!